Question

If the zeros of the Polynomial p(x)= x​​​​3​ -3x​​​2 +x+1 are m-n,m and m+n , find m and n.

Answer 1

Answer:

3

Step-by-step explanation:

f(x)=2x

2

+mx

2

+nx−14

(x−1)and(x+2) Factor at f(x)

x−1=0

⇒x=1

x+2=0

⇒x=−2

f(x)=2×1

3

+m×1

2

+1n−14

f(−2)=0

2(−2)

3

+m(−2)

2

+n(−2)−14=0

⇒0=2+m+n−14

⇒m+n=12−−−−(1)

−16+4m−2n=0

4m−2n−30=0

2(2m−n)=30

2m−n=15−−−−−(2)

on solving (i) & (ii) we get

m+n=12

2m−n=15

3m=27

m=

3

27

m=9

Now put m=9 in eqn(i) we have

⇒m+n=12

⇒9+n=12

⇒n=3

So,

n

m

=

3

9

=3